-6. The standard category-theory presentation of the monad laws
---------------------------------------------------------------
-In category theory, the monad laws are usually stated in terms of unit and join instead of unit and <=<.
+<pre>
+ γ = (φ G')
+ = ((unit <=< φ) G')
+ = ((join -v- (M unit) -v- φ) G')
+ = (join G') -v- ((M unit) G') -v- (φ G')
+ = (join G') -v- (M (unit G')) -v- γ
+ ??
+ = (unit G') <=< γ
+</pre>
+
+where as we said <code>γ</code> is a natural transformation from some `FG'` to `MG'`.
+
+Similarly, if <code>φ</code> is a natural transformation from `1C` to `MF'`, and <code>γ</code> is <code>(φ G)</code>, that is, a natural transformation from `G` to `MF'G`, then we can extend (iii.2) as follows:
+
+<pre>
+ γ = (φ G)
+ = ((φ <=< unit) G)
+ = (((join F') -v- (M φ) -v- unit) G)
+ = ((join F'G) -v- ((M φ) G) -v- (unit G))
+ = ((join F'G) -v- (M (φ G)) -v- (unit G))
+ ??
+ = γ <=< (unit G)
+</pre>
+
+where as we said <code>γ</code> is a natural transformation from `G` to some `MF'G`.
+
+
+
+
+The standard category-theory presentation of the monad laws
+-----------------------------------------------------------
+In category theory, the monad laws are usually stated in terms of `unit` and `join` instead of `unit` and `<=<`.